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Mingjie Zeng 2021S1 MZB125 Assignment PracticeQuiz2 due 01/04/2021 at 05:00pm Australia/Brisbane 1. (1 pt) Notation: Throughout this Quiz, vectors are denoted by com- ponents between angled brackets. ...

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ANSWERS SUBMITTED FOR QIZ 1  (3,4,-4)  (7,4,-6)  (10,8,-10)  (7,12,-11)  8.124038405 ANSWER SUBMITTED FOR QUIZ 2  5.385164807 UNITS ANSWERS SUBMITED FOR QUIZ 3  Two vecto ...

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ANSWERS SUBMITTED FOR QIZ 1  (3,4,-4)  (7,4,-6)  (10,8,-10)  (7,12,-11)  8.124038405 ANSWER SUBMITTED FOR QUIZ 2  5.385164807 UNITS ANSWERS SUBMITED FOR QUIZ 3  Two vecto ...

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CO 331: Coding Theory

Question

Answered

1. (10 marks) Let C be the cyclic binary (15, 9)-code generated by g(x) = 1 + x3 + x4 + x5 + x6
. It
is known that C is a 3-cyclic burst error correcting code. Decoding each of the following received
vectors using the error trapping algorithm that was presented in class.
(a) r1 = (10101 11010 11100).
(b) r2 = (11000 01110 10011).
(c) r3 = (01000 00010 11111).
2. (10 marks) Recall that if g(x) is the generator polynomial for an (n, k)-cyclic code C over GF(q),
then h∗(x) (where h(x) = (xn  1)/g(x)) is the generator polynomial for the dual code C⊥.
(a) Let xn ≤1 = g(x)h(x) over GF(q). Prove that a cyclic code C with generator polynomial g(x)
is self-orthogonal if and only if h∗(x) divides g(x).
(Recall that a linear code C is self-orthogonal if C ⊆ C⊥.)
(b) Give the generator polynomial for a self-orthogonal binary cyclic code of length n = 15.

CO 331: Coding Theory

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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

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Position Vector

Mingjie Zeng 2021S1 MZB125 Assignment PracticeQuiz2 due 01/04/2021 at 05:00pm Australia/Brisbane 1. (1 pt) Notation: Throughout this Quiz, vectors are denoted by com- ponents between angled brackets. Let a= h5 ;4 ; 5i and b= h 2;0 ; 1i. Compute: a + b= h , , i a b= h , , i 2 a = h , , i 3 a + 4b = ...

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Vector Components

Mingjie Zeng 2021S1 MZB125 Assignment PracticeQuiz2 due 01/04/2021 at 05:00pm Australia/Brisbane 1. (1 pt) Notation: Throughout this Quiz, vectors are denoted by com- ponents between angled brackets. Let a= h5 ;4 ; 5i and b= h 2;0 ; 1i. Compute: a + b= h , , i a b= h , , i 2 a = h , , i 3 a + 4b = ...

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Parallel and Non Parallel

ANSWERS SUBMITTED FOR QIZ 1  (3,4,-4)  (7,4,-6)  (10,8,-10)  (7,12,-11)  8.124038405 ANSWER SUBMITTED FOR QUIZ 2  5.385164807 UNITS ANSWERS SUBMITED FOR QUIZ 3  Two vectors parallel  Point same direction ANSWERS SUBMITTED FOR QUIZ 4  6.164414003  3.16227766 ...

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Vector Equation

ANSWERS SUBMITTED FOR QIZ 1  (3,4,-4)  (7,4,-6)  (10,8,-10)  (7,12,-11)  8.124038405 ANSWER SUBMITTED FOR QUIZ 2  5.385164807 UNITS ANSWERS SUBMITED FOR QUIZ 3  Two vectors parallel  Point same direction ANSWERS SUBMITTED FOR QUIZ 4  6.164414003  3.16227766 ...

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